Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16812657 |
| Fitting | C2×C4⋊C4×C109 ⋊ C2 |
| Sylow | C109 ⋊ C2×#117 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D109 |
| commutator | C2×C109 | C23×C4 |
| Frattini | C22 | C23×D109 |
| Fitting | C2×C4⋊C4×C109 | C2 |
| socle | C23×C109 | C23 |
| hypercenter | C2×C4⋊C4 | D109 |
| hypocenter | C109 | C2×#117 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28361345, #28361365, #28362747, … |
| maximal normal subgroup of | #28361345, #28361365, #28362747, … |
| maximal quotient of | C2×#20294871, C2×#20294873, C2×C4⋊C4×Dic109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1004);